A double-reliability RVFL bat optimization wind power interval prediction method and system

Abstract

The application discloses a double-reliability RVFL bat optimization wind power interval prediction method and system, specifically for: preprocessing wind farm historical power data, constructing a data set; establishing a basic RVFL, a cascaded enhanced RVFL and a direct connection enhanced RVFL candidate model, expressing the upper and lower bounds of the prediction interval as a linear combination of enhanced features and output weights; in the first stage, the hidden layer parameters are fixed, the output weights are solved by using an opportunity constraint optimization model containing a training set and a validation set coverage constraint, and the optimal basic model is selected according to the validation set SCORE index; in the second stage, the model parameters are used as elite prior solutions, a mixed initialization bat population is constructed by combining random exploration individuals, and the global network parameters are optimized; and the prediction interval is output on the test set and evaluated. The application improves the generalization coverage ability by double-reliability constraint, enhances the scene adaptability, and optimizes the network parameters by using a mixed initialization bat algorithm.

Description

Technical Field

[0001] This invention relates to the field of wind power range prediction technology, and in particular to a dual-reliability RVFL bat-optimized wind power range prediction method and system. Background Technology

[0002] Currently, the installed capacity of new energy sources such as wind power and photovoltaics continues to grow. The uncertainty of new energy output places higher demands on power system dispatching, reserve capacity allocation, power balance, and market transaction settlement. Wind power is affected by multiple factors such as wind speed, wind direction, turbulence, seasonal variations, and unit operating status, exhibiting significant randomness, non-stationarity, and volatility. Traditional point forecasting methods can only provide a single forecast value, failing to reflect the range of forecast errors and providing dispatchers with risk boundaries. Therefore, interval forecasting methods that can output upper and lower bounds of power output are gradually becoming an important research direction in new energy power forecasting.

[0003] Existing wind power range prediction methods can be broadly categorized into parametric and non-parametric methods. Parametric methods typically assume that the prediction error follows a Gaussian, Beta, or other specific probability distribution, and then construct the prediction range based on the distribution parameters. However, actual wind power errors often exhibit skewness, heavy tails, heteroscedasticity, and time-varying characteristics, and the assumption of a fixed distribution can easily lead to insufficient range coverage or excessively wide ranges. Non-parametric methods do not rely on pre-assumed error distributions and can directly learn the generation patterns of prediction ranges from historical data. These include quantile regression, direct range prediction using neural networks, Bayesian learning, and range prediction based on constrained optimization.

[0004] In neural network prediction models, deep networks possess strong nonlinear expressive power, but typically require a large number of parameters for training, resulting in long training times and strong dependence on sample size, hyperparameter settings, and computational resources. In contrast, Random Vector Functional Link (RVFL) networks are lightweight, shallow feedforward networks where the weights and biases from the input layer to the hidden layers are usually randomly generated and kept fixed, while the output layer weights are obtained through optimization. RVFLs are characterized by fast training speed, simple structure, and good generalization ability, making them suitable for wind power prediction scenarios with high real-time requirements. However, basic RVFL networks also have significant shortcomings. First, the random mapping parameters of the input layer are generated completely randomly, lacking an adaptive adjustment mechanism for wind power fluctuation characteristics, which can easily lead to invalid hidden nodes or redundant features, limiting the sharpness of interval predictions. Second, existing interval prediction models often rely primarily on training set coverage, which can lead to a situation where the coverage meets requirements during training but decreases during testing. Third, a single RVFL structure is difficult to adapt to wind power sequences under different seasons, fluctuation intensities, and sample complexities, and lacks an automatic model selection mechanism. Fourth, existing methods typically only optimize the output layer weights, failing to further optimize the randomly generated input layer weights and biases, thus limiting the model's performance.

[0005] Therefore, existing technologies still require a wind power interval prediction method that can balance interval coverage reliability, interval sharpness, model structure adaptability, and training efficiency under lightweight deployment conditions, in order to reduce the adverse effects of fixed random mapping parameters, single candidate structure, and overfitting due to training set coverage constraints. However, existing wind power interval prediction methods struggle to simultaneously ensure the reliability, sharpness, and training efficiency of the prediction interval under lightweight deployment conditions. While deep learning models can extract complex temporal features, they have many parameters and high training costs, making it difficult to meet the needs of rapid updates to the prediction model at the edge or site level. Traditional shallow neural networks, although fast in training, lack optimization for wind power data in their hidden layer random mapping, easily leading to insufficient or redundant feature representation and resulting in overly wide prediction intervals. Existing direct interval prediction methods based on chance constraints typically only focus on coverage constraints on training samples, resulting in insufficient coverage stability on validation or test sets, making it difficult to guarantee reliability in practical applications.

[0006] In addition, the following problems also exist:

[0007] 1) The random mapping parameters lack a secondary optimization mechanism.

[0008] In basic RVFL networks, the input layer weights and hidden layer biases are typically generated randomly and then fixed. While this method improves training speed, the randomly mapped parameters may not be suitable for the fluctuation patterns of the current wind power sequence, easily resulting in low-quality hidden features and limiting the effectiveness of output layer weight optimization.

[0009] 2) The candidate network structure lacks an automatic selection mechanism.

[0010] The degree of nonlinearity and the intensity of fluctuations in wind power sequences vary across different seasons and weather conditions. A single RVFL structure is difficult to adapt to all scenarios, and existing methods lack a mechanism for automatically selecting among candidate structures such as base RVFL, cascaded enhanced RVFL, and direct-connected enhanced RVFL.

[0011] 3) The reliability of the training set and the reliability of the validation set lack joint constraints.

[0012] Using training set coverage as a constraint alone can easily lead to overfitting. That is, the model achieves nominal coverage on the training set, but the coverage decreases on the validation or test set that is not involved in the solution, resulting in unstable interval prediction results in engineering applications.

[0013] 4) It is difficult to balance the quality of the initial solution in global optimization with population diversity.

[0014] When directly using swarm intelligence algorithms to optimize neural network parameters, if all initialization is randomized, the convergence speed is slow and it is easy to spend a long time searching for infeasible regions; if the search is only around existing feasible solutions, it is easy to get trapped in local optima. Therefore, a hybrid initialization strategy that balances the quality of feasible solutions and global exploration capability is needed. Summary of the Invention

[0015] The purpose of this invention is to provide a dual-reliability RVFL bat-optimized wind power interval prediction method, which can overcome the limitations of expressive power caused by fixed random parameters, improve the reliability of interval prediction, reduce the interval prediction SCORE, improve the overall performance of interval, and accelerate the convergence speed of the BA algorithm. It is applicable to different wind power prediction scenarios.

[0016] The technical solution to achieve the purpose of this invention is as follows: a dual-reliability RVFL bat-optimized wind power range prediction method, the steps of which are as follows:

[0017] Step 1, Data Acquisition and Sample Construction: Collect historical power data of the target wind farm, and process the historical power data sequentially by handling missing values, correcting outliers, and normalizing to obtain a normalized power sequence; construct input samples and prediction targets based on historical lagged power, and divide them into training set, validation set, and test set according to time order to obtain a dataset used for the first stage model solving, candidate model screening, second stage optimization, and final prediction evaluation;

[0018] Step 2: Construction of Candidate RVFL Interval Prediction Models: Using the input samples obtained in Step 1 as model input, and the Random Vector Functional Linked Network (RVFL) as the basic predictor, three types of candidate interval prediction models are constructed: basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL. Based on the network structure of each candidate model, corresponding enhancement feature matrices are generated, so that the upper and lower bounds of the prediction interval are represented as linear combinations of the enhancement feature matrices and the output weights, thus obtaining the candidate interval prediction expressions for solving the chance constraints.

[0019] Step 3, First-stage CPLEX Opportunity Constraint Model Construction: Based on fixing the hidden layer parameters and forming the enhanced feature matrix in Step 2, the upper and lower bounds of the prediction interval for each candidate interval prediction model are represented as a linear combination of the enhanced feature matrix and the output weights. For the three types of candidate models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—opportunity constraint optimization models are established with the goal of reducing the average width of the prediction interval. The opportunity constraint optimization model includes upper and lower bound legality constraints, training set coverage constraints, and validation set coverage constraints, so that the candidate interval prediction models meet the preset reliability requirements on both the training and validation sets.

[0020] Step 4, First-stage CPLEX solution and basic model selection: The CPLEX solver is used to solve the chance-constrained optimization model corresponding to each candidate model in Step 3. Under the condition of fixed hidden layer parameters, the optimal output weights of each candidate model are obtained, and the candidate models that satisfy the double reliability constraints are obtained. The SCORE index of each candidate model is calculated on the validation set. The SCORE index is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty. The candidate model with the smallest SCORE and that satisfies the reliability constraints is selected as the optimal basic model in the first stage. The hidden layer parameters and optimal output weights of the optimal basic model in the first stage are used as the source of elite prior solutions for the next stage hybrid initialization bat algorithm.

[0021] Step 5: Second-stage hybrid initialization and overall parameter optimization of the bat algorithm: Using the parameters of the optimal basic model obtained in Step 4 as the elite prior solution, and combining them with randomly explored individuals to construct a hybrid initialization bat population; the bat algorithm is used to iteratively optimize the overall network parameters of the optimal basic model in the first stage, including random mapping parameters, hidden layer biases, and output weights; after optimization, the final BA-ICCRVFL model is obtained, providing the final model parameters for interval prediction on the test set;

[0022] Step 6, Test Set Prediction and Evaluation: The BA-ICCRVFL model optimized in Step 5 is used for test set prediction. The upper and lower bounds of the wind power prediction interval for each test sample are output. The SCORE index, derived from Winklerscore, is used to evaluate the comprehensive performance of the prediction interval, and the wind power interval prediction results and evaluation results are obtained.

[0023] A dual-reliability RVFL bat-optimized wind power range prediction system is provided. This system is used to implement the aforementioned dual-reliability RVFL bat-optimized wind power range prediction method. The system includes:

[0024] The data preprocessing module is used to collect historical power data of the target wind farm, perform missing value processing, outlier correction and normalization processing on the historical power data, and construct input samples and prediction targets based on historical lagging power, and divide them into training set, validation set and test set according to time order.

[0025] The candidate RVFL model construction module is used to build three types of candidate interval prediction models, namely, basic RVFL, cascaded enhanced RVFL and direct enhanced RVFL, based on the random vector functional linking network RVFL as the predictor, randomly generate and fix the hidden layer parameters, and generate the corresponding enhanced feature matrix.

[0026] The CPLEX chance constraint output weight solving module is used to establish a chance constraint optimization model for each candidate model with the goal of reducing the average width of the prediction interval, and includes training set coverage constraints and validation set coverage constraints, under the condition that the hidden layer parameters are fixed. The CPLEX solver is used to solve for the optimal output weights of each candidate model.

[0027] The candidate model automatic selection module is used to calculate the SCORE index of each candidate model on the validation set. The SCORE index is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty, and select the candidate model with the smallest SCORE and that meets the reliability constraints as the optimal base model in the first stage.

[0028] The hybrid initialization BA overall parameter optimization module is used to construct a hybrid initialization bat population by using the parameters of the optimal basic model in the first stage as the elite prior solution, combined with random exploration individuals, and iteratively optimizing the overall network parameters using the bat algorithm to obtain the BA-ICCRVFL model.

[0029] The interval prediction output module is used to use the BA-ICCRVFL model for test set prediction, output the upper and lower bounds of the wind power prediction interval for each test sample, and evaluate the comprehensive performance of the prediction interval using the SCORE index.

[0030] Compared with the prior art, the significant advantages of this invention are:

[0031] (1) Improve the reliability of interval forecasts:

[0032] In the first stage, this invention uses CPLEX to solve the chance-constrained optimization model, directly constraining the coverage of the prediction interval, so that the basic model meets the nominal coverage requirement on the training set; at the same time, it further introduces the validation set coverage constraint to avoid the model being reliable only on training samples but with a decrease in coverage on unknown samples, thereby improving the generalization reliability of the interval prediction results.

[0033] (2) Reduce interval prediction SCORE and improve overall interval performance:

[0034] In the first stage, CPLEX finds the optimal output weights that satisfy the coverage constraint under the condition of fixed hidden layer parameters, so that the model can obtain a reliable basic prediction interval. In the second stage, the BA algorithm is used to further optimize the overall network parameters, including hidden layer weights, hidden layer biases and output weights, which can improve the quality of randomized mapped features, reduce redundant hidden features, and further compress the prediction interval width while ensuring the coverage requirement. At the same time, since SCORE considers both the interval width and the out-of-bounds penalty, the reduction of SCORE can reflect the overall improvement in the prediction interval quality.

[0035] (3) Overcoming the performance bottleneck of fixed random network parameters:

[0036] Traditional RVFL networks typically generate input layer weights and hidden layer biases randomly and then fix them, making the model performance highly susceptible to the quality of the random mapping. This invention uses a second-stage BA global optimization to optimize the overall network parameters, enabling the random mapping parameters of the hidden layers to be adjusted according to the characteristics of wind power data, thereby overcoming the limitations of expressive power caused by fixed random parameters.

[0037] (4) Improve the convergence efficiency of optimization:

[0038] The second stage of this invention adopts a hybrid initialization strategy, which uses the reliable model parameters obtained by CPLEX in the first stage as elite prior individuals, while retaining random exploration individuals. This strategy not only ensures that there are high-quality feasible solutions in the initial population, but also maintains the diversity of global search, which can accelerate the convergence speed of the BA algorithm and reduce the risk of getting trapped in local optima.

[0039] (5) Enhance the model's adaptability in different scenarios:

[0040] This invention sets up three candidate structures: basic RVFL, cascaded enhanced RVFL, and direct-connected enhanced RVFL. It automatically selects the optimal candidate model through the validation set SCORE index, enabling the model to adaptively select appropriate network complexity according to different seasons and different power fluctuation characteristics, thereby improving the applicability of the method in different wind power prediction scenarios. Attached Figure Description

[0041] Figure 1 This is a flowchart of the overall process for predicting wind power range in two stages according to the present invention.

[0042] Figure 2 The flowchart for optimizing the overall network parameters of the bat algorithm in the second stage of hybrid initialization.

[0043] Figure 3 The plot showing the prediction intervals generated by the BA-ICCRVFL model based on the spring dataset.

[0044] Figure 4 The plot shows the prediction intervals generated by the BA-ICCRVFL model based on the summer dataset.

[0045] Figure 5 A plot showing the prediction intervals generated by the BA-ICCRVFL model based on the fall dataset.

[0046] Figure 6 The plot shows the prediction intervals generated by the BA-ICCRVFL model based on the winter dataset.

[0047] Figure 7 The diagram illustrates the iterative optimization process of the second-stage hybrid initialization bat algorithm based on the winter dataset. Detailed Implementation

[0048] To address the shortcomings of existing wind power range prediction methods, this invention proposes a wind power range prediction method and system based on a dual-reliability-constrained stochastic vector functional linked network (RVFL) and hybrid initialization bat optimization. This method uses the RVFL network as the basic predictor and constructs three types of candidate range prediction models: basic RVFL, cascaded enhanced RVFL, and direct-connected enhanced RVFL. In the first stage, randomly generated hidden layer parameters are fixed, and the chance-constrained optimization model is solved using a CPLEX solver. The optimal output weights of each candidate model are calculated, and a basic feasible model is selected based on reliability constraints on the training and validation sets. In the second stage, the feasible model parameters obtained in the first stage are used as elite prior solutions. A hybrid initialization bat population is constructed using randomly explored individuals to globally optimize the stochastic mapping parameters and output layer parameters of the RVFL network, further shortening the average width of the prediction range while meeting reliability requirements.

[0049] For ease of description, the dual reliability constraint RVFL candidate model constructed in the first stage of this invention is collectively referred to as ICCRVFL, and the model optimized by the bat algorithm (BA) in the second stage is referred to as BA-ICCRVFL.

[0050] Combination Figure 1 This invention provides a dual-reliability RVFL bat-optimized wind power range prediction method, the steps of which are as follows:

[0051] Step 1, Data Acquisition and Sample Construction: Collect historical power data of the target wind farm, and process the historical power data sequentially by handling missing values, correcting outliers, and normalizing to obtain a normalized power sequence; construct input samples and prediction targets based on historical lagged power, and divide them into training set, validation set, and test set according to time order to obtain a dataset used for the first stage model solving, candidate model screening, second stage optimization, and final prediction evaluation;

[0052] Step 2: Construction of Candidate RVFL Interval Prediction Models: Using the input samples obtained in Step 1 as model input, and the Random Vector Functional Linked Network (RVFL) as the basic predictor, three types of candidate interval prediction models are constructed: basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL. Based on the network structure of each candidate model, corresponding enhancement feature matrices are generated, so that the upper and lower bounds of the prediction interval are represented as linear combinations of the enhancement feature matrices and the output weights, thus obtaining the candidate interval prediction expressions for solving the chance constraints.

[0053] Step 3, First-stage CPLEX Opportunity Constraint Model Construction: Based on fixing the hidden layer parameters and forming the enhanced feature matrix in Step 2, the upper and lower bounds of the prediction interval for each candidate interval prediction model are represented as a linear combination of the enhanced feature matrix and the output weights. For the three types of candidate models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—opportunity constraint optimization models are established with the goal of reducing the average width of the prediction interval. The opportunity constraint optimization model includes upper and lower bound legality constraints, training set coverage constraints, and validation set coverage constraints, so that the candidate interval prediction models meet the preset reliability requirements on both the training and validation sets.

[0054] Step 4, First-stage CPLEX solution and basic model selection: The CPLEX solver is used to solve the chance-constrained optimization model corresponding to each candidate model in Step 3. Under the condition of fixed hidden layer parameters, the optimal output weights of each candidate model are obtained, and the candidate models that satisfy the double reliability constraints are obtained. The SCORE index of each candidate model is calculated on the validation set. The SCORE index is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty. The candidate model with the smallest SCORE and that satisfies the reliability constraints is selected as the optimal basic model in the first stage. The hidden layer parameters and optimal output weights of the optimal basic model in the first stage are used as the source of elite prior solutions for the next stage hybrid initialization bat algorithm.

[0055] Step 5: Second-stage hybrid initialization and overall parameter optimization of the bat algorithm: Using the parameters of the optimal basic model obtained in Step 4 as the elite prior solution, and combining them with randomly explored individuals to construct a hybrid initialization bat population; the bat algorithm is used to iteratively optimize the overall network parameters of the optimal basic model in the first stage, including random mapping parameters, hidden layer biases, and output weights; after optimization, the final BA-ICCRVFL model is obtained, providing the final model parameters for interval prediction on the test set;

[0056] Step 6, Test Set Prediction and Evaluation: The BA-ICCRVFL model optimized in Step 5 is used for test set prediction. The upper and lower bounds of the wind power prediction interval for each test sample are output. The SCORE index, derived from Winklerscore, is used to evaluate the comprehensive performance of the prediction interval, and the wind power interval prediction results and evaluation results are obtained.

[0057] As a specific example, in step 1, linear interpolation is used to fill in consecutive missing values; forward padding or backward padding is used to fill in missing values ​​at the beginning or end of the sequence; and outliers that are significantly outside the range of installed capacity are truncated to a reasonable power range.

[0058] Historical power data of the target wind farm over a continuous time period is collected. This historical power data includes timestamps and actual active power values. The historical power data is then sorted according to the timestamps to form an original power time series. Subsequently, the original power time series is preprocessed. For consecutive missing values ​​in the middle of the series, linear interpolation is used to fill in the missing values. For missing values ​​at the beginning or end of the series, forward or backward padding is used. Abnormal power values ​​less than zero or exceeding the wind farm's installed capacity are corrected or truncated to a reasonable power range.

[0059] After preprocessing, the power sequence is normalized to the specified values ​​using the Min-Max method. The power sequence is normalized to reduce the impact of different power units and numerical ranges on subsequent model training. Based on the normalized power sequence, input samples and prediction targets are constructed according to historical lag power. For prediction time t, the normalized power values ​​of the previous N times are used as the input feature vector, and the normalized power value of the current time is used as the prediction target. Finally, the constructed samples are divided into training set, validation set, and test set according to time order. The training set is used for solving the opportunity-constrained model in the first stage, the validation set is used for candidate model selection and parameter optimization in the second stage, and the test set is used for final interval prediction and performance evaluation, thus obtaining the dataset required for subsequent modeling.

[0060] Furthermore, step 1 specifically includes the following steps:

[0061] Step 1.1: Collect historical power data of the target wind farm over a continuous time period. The historical power data includes timestamps and actual active power values. Sort the historical power data according to the timestamp order to form the original power time series.

[0062] Step 1.2: Preprocess the original power time series: For continuous missing values ​​in the middle of the series, use linear interpolation to fill them in; for missing values ​​at the beginning or end of the series, use forward filling or backward filling; for abnormal power values ​​that are less than zero or exceed the installed capacity range of the wind farm, correct or truncate the abnormal power values ​​to the set power range.

[0063] Step 1.3: After preprocessing, the power time series is normalized to the [0,1] interval using the Min-Max method, resulting in the normalized power time series. The normalization formula is:

[0064]

[0065] in, Let be the original power value at time t. Let be the normalized power value at time t. , These are the minimum and maximum power values ​​in the training data, respectively.

[0066] Step 1.4: Construct input samples and prediction targets based on the normalized power time series: For prediction time t, the normalized power values ​​of the previous N times form the input feature vector, and the normalized power value at time t is used as the input feature vector. As the prediction target, the expression is:

[0067]

[0068]

[0069] in, Let be the input feature vector of the t-th sample. Let N be the prediction target for the t-th sample; N is the lag order, which is determined by the partial autocorrelation function, validation set search, or fixed historical window length.

[0070] Step 1.5: Divide the constructed samples into training set, validation set and test set according to time order. The training set is used for solving the opportunity constraint model in the first stage, the validation set is used for candidate model screening and parameter optimization in the second stage, and the test set is used for final interval prediction and performance evaluation.

[0071] As a specific example, in step 2, the input samples obtained in step 1 are used as the model input, and the Random Vector Functional Linked Network (RVFL) is used as the basic predictor. The weight matrix from the input layer to the hidden layer and the bias vector of the hidden layer are randomly generated, and the hidden layer parameters are kept fixed in the first stage. Based on the input sample matrix, the hidden layer output matrix, and different candidate network structures, three types of candidate interval prediction models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—are constructed respectively.

[0072] For the basic RVFL structure, the input sample features and the first hidden layer features are used together as enhancement features to generate the upper and lower bounds of the prediction interval. For the cascaded enhancement RVFL structure, a second hidden layer is set after the first hidden layer, and the output features of the second hidden layer are used to generate the upper and lower bounds of the prediction interval. For the direct-connection enhancement RVFL structure, the connections from the input sample features, the first hidden layer features, and the second hidden layer features to the output layer are preserved and combined to form the enhancement feature matrix. For any candidate model, the lower and upper bounds of the prediction interval are represented as linear combinations of the enhancement feature matrix and the corresponding output weights. A validity constraint is set that the lower bound is no greater than the upper bound and the upper and lower bounds are within the normalized power range. This yields three types of candidate interval prediction expressions that can be used to solve the opportunity constraint in the first stage.

[0073] Furthermore, step 2 specifically includes the following steps:

[0074] Step 2.1: Set the input sample matrix for:

[0075]

[0076] in, Let T be the input feature vector of the t-th sample, and T be the number of samples.

[0077] Step 2.2: Let the random weight matrix from the input layer to the first hidden layer be... The bias vector of the first hidden layer is The nonlinear activation function is Then the output matrix of the first hidden layer for:

[0078]

[0079] in, This only represents the hidden layer bias term. This is a column vector with all elements equal to 1, used for hidden layer feature calculation, and does not represent the output layer bias;

[0080] Step 2.3: For any candidate model m, let the enhanced feature matrix be denoted as . The output weight matrix is The output weight matrix Including the lower bound of the prediction interval output weight Output weights and the upper bound of the prediction interval The expressions for the lower and upper bounds of the prediction interval are:

[0081]

[0082]

[0083] in, Let be the lower bound vector of the prediction interval for candidate model m. Let be the upper bound vector of the prediction interval for candidate model m. Let m be the enhanced feature matrix of the candidate model. To predict the lower bound of the interval, output weights. Output weights to predict the upper bound of the interval;

[0084] For the t-th sample, we have:

[0085]

[0086]

[0087] in, and Let be the lower bound and the upper bound of the prediction interval for the t-th sample under the candidate model m, respectively. Let be the enhanced feature vector of the t-th sample under the candidate model m;

[0088] Step 2.4: To ensure the validity of the output interval, the following constraints are applied to each sample:

[0089]

[0090] Furthermore, the specific method for constructing the three types of candidate interval prediction models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—in step 2 is as follows:

[0091] (1) Basic RVFL structure

[0092] Enhanced feature matrix of basic RVFL Defined as the output matrix of the first hidden layer With input sample matrix The concatenation expression is:

[0093]

[0094] Lower bound of the prediction interval for the basic RVFL and the upper bound of the prediction interval Generated from output layer weights:

[0095]

[0096]

[0097] In the formula, The lower bound of the prediction interval for the basic RVFL is output as the weight. Output weights as the upper bound of the prediction interval for the basic RVFL;

[0098] (2) Cascaded Enhanced RVFL Structure

[0099] Cascaded Enhancement RVFL adds a second hidden layer after the base hidden layer. Let the weight matrix from the first hidden layer to the second hidden layer be... The bias vector of the second hidden layer is Then the output matrix of the second hidden layer for:

[0100]

[0101] Enhanced feature matrix of cascaded enhanced RVFL The expression is:

[0102]

[0103] Lower bound of the prediction interval for cascaded enhanced RVFL and the upper bound of the prediction interval Generated from the output features of the second hidden layer:

[0104]

[0105]

[0106] In the formula, To enhance the lower bound of the prediction interval of cascaded RVFL, output weights. Output weights for the upper bound of the prediction interval of the cascaded enhanced RVFL;

[0107] (3) Direct-connected reinforced RVFL structure

[0108] Direct-connection enhanced RVFL preserves the connections from the input layer, the first hidden layer, and the second hidden layer to the output layer. The enhanced feature matrix of the direct-connection enhanced RVFL... For the input sample matrix First hidden layer output matrix Second hidden layer output matrix The concatenation expression is:

[0109]

[0110] Lower bound of prediction interval for direct-connected enhanced RVFL and the upper bound of the prediction interval The expression is:

[0111]

[0112]

[0113] In the formula, To directly enhance the lower bound of the prediction interval of the RVFL, output weights. Output weights to enhance the upper bound of the prediction interval for direct connection to RVFL.

[0114] This structure takes into account the original historical power information, shallow random features, and deep combined features, which can reduce the loss of information in multi-layer mapping and is suitable for power sequences with obvious seasonal changes or many mutations.

[0115] As a specific example, step 3 calculates the optimal output weights for each candidate model, as follows:

[0116] Based on the fixed hidden layer parameters and the obtained enhanced feature matrices of each candidate model in step 2, the parameters to be determined for each candidate model are limited to the lower bound output weights and the upper bound output weights of the prediction interval. For each type of candidate interval prediction model, a chance-constrained optimization model is established with the objective of reducing the average width of the prediction interval, so that the model can improve the sharpness of the interval prediction as much as possible while meeting the coverage requirements.

[0117] The opportunity-constrained optimization model includes interval upper and lower bound validity constraints, sample coverage relationship constraints, training set coverage constraints, and validation set coverage constraints. The interval upper and lower bound validity constraints ensure that the lower bound of the prediction interval is no greater than the upper bound, and that the prediction interval lies within the normalized power range. The sample coverage relationship constraints introduce binary coverage variables and use Big-M form to represent whether the actual power falls within the prediction interval. The training set coverage constraints ensure that the proportion of actual power falling within the prediction interval in the training samples is no less than the nominal coverage rate. The validation set coverage constraints ensure that the model still meets the preset reliability requirements on validation samples that are not directly solved for output weights. Through these constraints, the dual reliability requirements of interval prediction are transformed into a mixed-integer linear programming problem that can be handled by the CPLEX solver.

[0118] Furthermore, the specific construction method of the opportunity-constrained optimization model in step 3 is as follows:

[0119] Step 3.1: Assume the nominal coverage is PINC, and the allowable false negative rate is... satisfy:

[0120]

[0121] Step 3.2: Introduce binary overriding variables , is used to indicate whether the t-th sample is covered by the prediction interval, and is expressed as:

[0122]

[0123] in, and Let be the lower bound and the upper bound of the prediction interval for the t-th sample under the candidate model m, respectively. This represents the actual power value of the t-th sample.

[0124] Step 3.3: Use Big-M constraints to characterize the coverage relationship:

[0125]

[0126]

[0127] in, For a constant greater than the set value, since the power value has been normalized to [0,1], we take:

[0128]

[0129] Step 3.4, the legality constraints for the prediction interval are:

[0130]

[0131] Step 3.5, the training set coverage constraint is:

[0132]

[0133] in, The training set is the set of sample indices. The number of samples in the training set;

[0134] Step 3.6, the validation set coverage constraint is:

[0135]

[0136] in, To verify the reliability tolerance coefficient of the set, The set of sample indices for the validation set. The number of samples in the validation set;

[0137] Step 3.7: For candidate model m, the chance-constrained optimization model solved by CPLEX in the first stage is as follows:

[0138]

[0139] in, To predict the lower bound of the interval, output weights. Output weights to predict the upper bound of the interval; Let be the enhanced feature vector of the t-th sample under the candidate model m.

[0140] As a specific example, step 4 involves selecting basic feasible models, as detailed below:

[0141] The CPLEX solver is used to solve the opportunity-constrained optimization models corresponding to the three types of candidate models: basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL. Under the condition that the hidden layer parameters are fixed, the optimal output weights of each candidate model are obtained. Based on the optimal output weights, the upper and lower bounds of the prediction interval of each candidate model on the training set and validation set are calculated, and it is determined whether they simultaneously satisfy the training set coverage constraint and the validation set coverage constraint. Candidate models that satisfy the dual reliability constraint are retained.

[0142] For candidate models that satisfy the dual reliability constraints, the SCORE index is calculated on the validation set. The SCORE index, derived from the Winkler score, is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty when the actual power falls outside the prediction interval. When the prediction interval is narrow and the actual power does not exceed the limit, the SCORE value is small; when the actual power is below the lower bound or above the upper bound of the prediction interval, the SCORE value increases with the degree of out-of-bounds violation. The average SCORE of each candidate model on the validation set is compared, and the candidate model with the smallest SCORE that satisfies the reliability constraints is selected as the optimal base model for the first stage. The hidden layer parameters of this model, along with the optimal output weights obtained by CPLEX, are used as the elite prior solution source for the hybrid initialization bat algorithm in the next stage.

[0143] Furthermore, after the CPLEX solution is completed in step 4, the optimal output weights of the candidate model m are obtained. for:

[0144]

[0145] The constraints in step 3.7 are satisfied;

[0146] The corresponding prediction interval is:

[0147]

[0148]

[0149] in, Output weights for the lower bound of the optimal prediction interval of candidate model m. Output weights for the upper bound of the optimal prediction interval of candidate model m. and These are the lower bound and upper bound of the optimal prediction interval for the t-th sample under the candidate model m, respectively.

[0150] Furthermore, the specific method for calculating the SCORE index of each candidate model and automatically filtering it in step 4 is as follows:

[0151] Initialization and CPLEX solutions were performed on the three candidate structures to obtain three sets of candidate models that satisfy the dual reliability constraint. For each candidate model, its validation set SCORE was calculated. This SCORE metric, derived from the Winkler score, is used to evaluate the prediction interval width and the penalty for out-of-bounds samples.

[0152] For validation set sample t, the one-sample SCORE of candidate model m is:

[0153]

[0154] in, The SCORE value of candidate model m on the validation set sample t; This is an indicator function that takes the value 1 if the condition within the parentheses is true, and 0 otherwise.

[0155] The average SCORE of candidate model m on the validation set is:

[0156]

[0157] Right now:

[0158]

[0159] in, The average SCORE value of candidate model m on the validation set;

[0160] Among the three candidate models, the model with the smallest SCORE is selected as the optimal base model for the first stage:

[0161]

[0162] in, Represents the set of candidate models:

[0163]

[0164] in, These represent the basic RVFL, cascaded enhancement RVFL, and direct-connect enhancement RVFL, respectively. This is the sequence number of the optimal basic model in the first stage.

[0165] As a specific example, in step 5, the feasible model parameters obtained in the first stage are used as the elite prior solution. Combined with the construction of a mixed initial bat population through random exploration individuals, the random mapping parameters and output layer parameters of the RVFL network are globally optimized. Specifically, this includes:

[0166] Using the optimal base model obtained in step 4 as the optimization object, its hidden layer weights, hidden layer biases, and output weights are combined to form the overall network parameter vector. For candidate structures containing a second hidden layer, the overall network parameter vector also includes the weights from the first hidden layer to the second hidden layer and the second hidden layer bias. In the second stage, instead of optimizing only the output weights, the bat algorithm is used to jointly optimize the overall network parameters, with minimizing the validation set SCORE as the fitness objective.

[0167] During bat population initialization, the parameter vector of the optimal basic model from the first stage is used as the elite prior solution, and a small random perturbation is added to its neighborhood to form elite prior individuals. At the same time, other individuals are randomly generated within the preset parameter search range to form random exploration individuals. The elite prior individuals and random exploration individuals together constitute a hybrid initialized bat population, which ensures that the initial population inherits the reliability of the feasible model from the first stage while maintaining the diversity required for global search.

[0168] During iterative optimization, the position of each bat represents a global network parameter vector, and the velocity represents the parameter update direction. New candidate parameter vectors are generated by updating the frequency, velocity, position, loudness, and impulse emission rate. For each candidate parameter vector, the hidden layer output, augmented feature matrix, upper and lower bounds of the prediction interval, and validation set SCORE are recalculated, and the acceptance of new candidate solutions is determined based on the fitness results. When the maximum number of iterations is reached, or when the decrease in validation set SCORE is less than a preset threshold over several consecutive generations, iteration stops, the optimal global network parameters are output, and the final BA-ICCRVFL model is obtained.

[0169] Furthermore, the specific method for optimizing the overall parameters of the hybrid initialization bat algorithm in step 5 is as follows:

[0170] Step 5.1: Read the parameters of the optimal base model in the first stage and use them as the elite prior vector. The elite prior vector It includes the stochastic hidden layer parameters of the first-stage optimal model and the optimal output weights obtained by CPLEX;

[0171] Step 5.2, Mixed Initialization of Bat Population: Let the size of the bat population be B, and divide the population into two categories: elite prior individuals and random exploratory individuals;

[0172] Elite prior individuals are generated by copying the parameter vector of the optimal basic model in the first stage and adding a small Gaussian perturbation, as expressed in the following expression:

[0173]

[0174] in, For the first An elite a priori individual, For the disturbance intensity, It is a random vector that follows a standard normal distribution; For the number of elite prior individuals; superscript This indicates that the 0th iteration is the initialization.

[0175] Randomly explored individuals are generated randomly within the allowed parameter range, and the expression is:

[0176]

[0177] in, For the first A random exploration individual, and These are the lower and upper bounds for parameter search, respectively. Let be a random vector whose elements are located in the interval [0,1]. This represents element-wise multiplication; To randomly explore the number of individuals;

[0178] Let the proportion of elite prior individuals be... The number of elite prior individuals is:

[0179]

[0180] The number of individuals to be randomly explored is:

[0181]

[0182] Step 5.3: Iteratively optimize the overall network parameters using the bat algorithm;

[0183] Let the frequency of the i-th bat in the k-th iteration be... ,speed and location Updated to:

[0184]

[0185]

[0186]

[0187] in, and These are the minimum and maximum frequencies, respectively. A random number in the interval [0,1]. Let be the optimal parameter vector that minimizes the objective function value on the validation set in the population during the (k-1)th iteration. Let be the speed of the i-th bat in the (k-1)th iteration. Let i be the position of the i-th bat in the (k-1)th iteration;

[0188] During the local search phase, candidate solutions are generated centered on the current optimal solution:

[0189]

[0190] in, As a candidate solution, A random number in the interval [0,1]. The average loudness of the current population at the k-th iteration; This is the optimal parameter vector that minimizes the objective function value of the validation set in the population at the k-th iteration.

[0191] If the objective function value of a candidate solution is better than the current solution, and the random number is less than the current loudness, then the candidate solution is accepted, and the loudness is updated. and pulse emission rate :

[0192]

[0193]

[0194] in, This is the loudness attenuation coefficient. Here, k is the pulse emission rate growth coefficient, and k is the current iteration number. , Let be the loudness of the i-th bat in the k-th and (k+1)-th iterations, respectively. Let be the pulse emission rate of the i-th bat in the (k+1)-th iteration. The initial pulse emission rate;

[0195] Step 5.4: When the maximum number of iterations is reached or the objective function on the validation set decreases by less than the convergence threshold for several consecutive generations, stop the iteration and output the optimal overall network parameters. .

[0196] As a specific example, in step 6, the BA-ICCRVFL model obtained in step 5 is used for test set prediction. For each input sample in the test set, the corresponding enhanced feature matrix is ​​calculated using the overall network parameters optimized in the second stage. The lower bound and upper bound of the wind power prediction interval for that test sample are generated by the enhanced feature matrix and the output weights, thereby obtaining the wind power interval prediction results for each time step in the test set.

[0197] After obtaining the prediction interval for the test set, the SCORE index, derived from the Winkler score, is used to evaluate the overall performance of the prediction interval. The SCORE index considers both the prediction interval width and the coverage violation penalty. When the actual power is within the prediction interval, the prediction interval width is primarily evaluated; when the actual power is below the lower bound or above the upper bound of the prediction interval, a penalty term related to the distance of the boundary violation is introduced. The average SCORE of all samples in the test set is calculated as the overall evaluation result of the BA-ICCRVFL model on the test set; a smaller SCORE indicates better overall performance in terms of reliable coverage and interval sharpness.

[0198] Furthermore, the specific methods for test set prediction and evaluation in step 6 are as follows:

[0199] The optimal network parameters obtained in the second stage optimization For test set Predict and output the prediction range for each test sample:

[0200]

[0201] The SCORE metric, derived from the Winkler score, is used as the evaluation metric. For a single sample t in the test set, the single-sample SCORE is:

[0202]

[0203] The average SCORE of the test set is :

[0204]

[0205] in, The number of samples in the test set. SCORE is the value of the test set sample t. A smaller SCORE indicates a better overall performance in terms of prediction interval width and coverage violation penalty.

[0206] This invention also provides a dual-reliability RVFL bat-optimized wind power range prediction system, which is used to implement the aforementioned dual-reliability RVFL bat-optimized wind power range prediction method. The system includes:

[0207] The data preprocessing module is used to collect historical power data of the target wind farm, perform missing value processing, outlier correction and normalization processing on the historical power data, and construct input samples and prediction targets based on historical lagging power, and divide them into training set, validation set and test set according to time order.

[0208] The candidate RVFL model construction module is used to build three types of candidate interval prediction models, namely, basic RVFL, cascaded enhanced RVFL and direct enhanced RVFL, based on the random vector functional linking network RVFL as the predictor, randomly generate and fix the hidden layer parameters, and generate the corresponding enhanced feature matrix.

[0209] The CPLEX chance constraint output weight solving module is used to establish a chance constraint optimization model for each candidate model with the goal of reducing the average width of the prediction interval, and includes training set coverage constraints and validation set coverage constraints, under the condition that the hidden layer parameters are fixed. The CPLEX solver is used to solve for the optimal output weights of each candidate model.

[0210] The candidate model automatic selection module is used to calculate the SCORE index of each candidate model on the validation set. The SCORE index is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty, and select the candidate model with the smallest SCORE and that meets the reliability constraints as the optimal base model in the first stage.

[0211] The hybrid initialization BA overall parameter optimization module is used to construct a hybrid initialization bat population by using the parameters of the optimal basic model in the first stage as the elite prior solution, combined with random exploration individuals, and iteratively optimizing the overall network parameters using the bat algorithm to obtain the BA-ICCRVFL model.

[0212] The interval prediction output module is used to use the BA-ICCRVFL model for test set prediction, output the upper and lower bounds of the wind power prediction interval for each test sample, and evaluate the comprehensive performance of the prediction interval using the SCORE index.

[0213] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0214] Example 1

[0215] like Figure 1 As shown, the overall process of the two-stage wind power range prediction of this invention includes data acquisition and sample construction, construction of candidate RVFL range prediction models, first-stage CPLEX chance constraint solution and basic model screening, second-stage hybrid initialization bat algorithm overall parameter optimization, and test set prediction and evaluation. Figure 1 The data preprocessing and sample partitioning correspond to step 1; candidate model construction corresponds to step 2; CPLEX chance constraint modeling and solution screening corresponds to steps 3 and 4; BA overall parameter optimization corresponds to step 5; and test set prediction and evaluation corresponds to step 6.

[0216] like Figure 2 As shown, the second-stage hybrid initialization bat algorithm's overall network parameter optimization process includes: reading the optimal basic model parameters from the first stage, using them as elite prior individuals and adding a small perturbation; generating random exploration individuals according to a preset ratio; forming an initial bat population from the elite prior individuals and random exploration individuals; updating frequency, velocity, location, loudness, and impulse emission rate in each iteration, and using the validation set SCORE as a fitness function to evaluate candidate parameters; and outputting the optimal overall network parameters when the maximum number of iterations or the convergence threshold condition is met.

[0217] Figures 3-6The prediction intervals generated by the BA-ICCRVFL model are presented for spring, summer, autumn, and winter datasets, respectively. Each figure illustrates that the present invention can output prediction intervals that include the actual power change trend under different seasons and different wind power fluctuation characteristics. These figures are also used to verify the reliability and sharpness of the interval predictions in conjunction with test set metrics such as SCORE, PICP, and PINAW.

[0218] This method includes the following steps:

[0219] 1. Data acquisition and sample construction;

[0220] Historical power data of the target wind farm is collected, including timestamps and actual active power values. The original power sequence undergoes missing value processing, outlier correction, and normalization. For consecutive missing values, linear interpolation is used for completion; for missing values ​​at the beginning or end of the sequence, forward or backward padding is used; for outliers significantly exceeding the installed capacity range, they are truncated to a reasonable power range.

[0221] The power sequence was normalized to the [0,1] interval using the Min-Max method;

[0222] Input samples are constructed based on historical lag power. For prediction time t, the power values ​​of the previous N times are used as the input vector, and the power at the current time is used as the prediction target. The samples are divided into training set, validation set and test set according to time order. The training set is used to solve the basic model parameters, the validation set is used for candidate model selection and second-stage optimization, and the test set is used for final performance evaluation.

[0223] 2. Construct a basic model for RVFL interval prediction;

[0224] The basic RVFL network consists of an input layer, a random hidden layer, and an output layer. In this invention, the final output layer does not have a bias term; the prediction interval is obtained solely by multiplying the enhanced feature matrix and the output weight matrix.

[0225] To ensure the validity of the output range, constraints are imposed on each sample.

[0226] 3. Construct three types of candidate RVFL interval prediction structures;

[0227] To adapt to different wind power fluctuation complexities, this invention constructs three types of candidate RVFL interval prediction structures, namely, basic RVFL, cascaded enhanced RVFL, and direct-connected enhanced RVFL.

[0228] 1) The basic RVFL structure has fewer structural parameters and faster training speed, making it suitable for scenarios with relatively stable power fluctuations.

[0229] 2) Cascaded enhanced RVFL structure, which enhances feature representation capability through cascaded nonlinear mapping, is suitable for wind power sequences with strong fluctuations or more complex nonlinear relationships.

[0230] 3) Direct-connected enhanced RVFL structure, which takes into account the original historical power information, shallow random features and deep combined features, can reduce the loss of information in multi-layer mapping, and is suitable for power sequences with obvious seasonal changes or many mutations.

[0231] 4. Solve the opportunity constraint in the first stage and output the weights;

[0232] In the first stage, for each candidate model, its hidden layer parameters are first randomly generated and then fixed. For the basic RVFL, this step can be omitted. After fixing the hidden layer parameters, the enhanced feature matrix of the candidate model m can be obtained, and the model output is related to the output weights. and The form is linear. Therefore, this invention uses the CPLEX solver to solve the chance-constrained optimization model and calculates the optimal output weights of the candidate model;

[0233] The goal of interval prediction is to make the prediction interval as narrow as possible while ensuring that the probability of the actual power falling into the prediction interval is not lower than that of PINC.

[0234] After CPLEX is completed, the optimal output weights of the candidate model m are obtained:

[0235]

[0236] Therefore, for candidate model m, this invention transforms the prediction interval coverage constraint into a mixed integer linear programming model, and uses the CPLEX solver to solve the model to obtain the optimal output weights of the candidate model.

[0237] 5. Automatic selection of candidate models in the first stage

[0238] Initialization and CPLEX solutions were performed on the three candidate structures to obtain three sets of candidate models that satisfy the dual reliability constraint. For each candidate model, its validation set SCORE was calculated. This SCORE metric, derived from the Winkler score, is used to evaluate the prediction interval width and the penalty for out-of-bounds samples.

[0239] Among the three candidate models, the SCORE minimum model was selected as the optimal base model for the first stage:

[0240]

[0241] in, Represents the set of candidate models:

[0242]

[0243] This model not only has a narrow prediction range on the validation set, but also meets the preset reliability requirements for coverage, and can be used as a priori feasible solution for the second-stage global parameter optimization.

[0244] 6. Construct a second-stage bat algorithm to optimize overall network parameters.

[0245] In the first stage, CPLEX solves only the output weights with fixed hidden layer parameters. Although this yields a basic prediction interval that satisfies the coverage constraint, the hidden layer weights and biases are still randomly initialized. To further enhance feature representation capabilities, this invention employs BA in the second stage to optimize the optimal candidate model m selected in the first stage. * The overall network parameters are jointly optimized, including the input layer to hidden layer weights, hidden layer biases, second hidden layer weights, second hidden layer biases, and output weights.

[0246] The parameters optimized in the second stage are no longer limited to output weights, but include the overall network parameters: hidden layer weights, hidden layer biases, and output weights.

[0247] The second-stage optimization objective is to minimize the validation set SCORE. In this stage, for each candidate parameter vector generated by BA, the hidden layer output, augmented feature matrix, upper and lower bounds of the prediction interval, and validation set SCORE are recalculated based on that parameter, thereby achieving joint optimization of the overall network parameters.

[0248] It should be noted that the SCORE index is derived from the interval evaluation concept of the Winkler score and is only used as the fitness function and prediction result evaluation index of the BA algorithm, and is not considered as an innovative technical feature of this invention.

[0249] 7. Initialize a mixed bat population

[0250] To avoid the slow convergence and scarcity of feasible solutions caused by random initialization in traditional swarm intelligence algorithms, this invention proposes a hybrid initialization strategy. Let the bat population size be B, and divide the population into two categories: elite prior individuals and randomly exploratory individuals.

[0251] Let the proportion of elite prior individuals be... The number of elite prior individuals is: ;

[0252] The number of individuals to be randomly explored is: ;

[0253] in, The percentage can be set to 20% to 40%, and the percentage of randomly explored individuals can be set to 60% to 80%. In practical applications, this percentage can be adjusted according to the data scale and model complexity.

[0254] 8. Bat Algorithm Parameter Update

[0255] The position of each bat represents a network parameter vector. Speed ​​indicates the direction of parameter update. The bat algorithm searches for optimal parameters by iteratively updating frequency, velocity, location, loudness, and pulse emission rate.

[0256] When the maximum number of iterations is reached, or when the objective function on the validation set decreases by less than a threshold for several consecutive iterations, the iteration stops and the optimal parameters are output. .

[0257] 9. Test Set Prediction and Evaluation

[0258] The optimal network parameters obtained from the second-stage optimization are used for test set prediction, outputting the prediction interval for each test sample. This invention uses SCORE, derived from the Winkler score, as the primary evaluation metric. A smaller SCORE indicates better overall performance in terms of prediction interval width and coverage violation penalty.

[0259] Example 2

[0260] 1) Experimental data

[0261] This embodiment uses publicly available operational data from a European offshore wind farm for experimentation. The data time resolution is 15 minutes, and the data fields include timestamps and the actual active power of the wind farm. To verify the applicability of the method of this invention under different seasonal wind power fluctuation scenarios, the original data is divided into four datasets according to the season: spring (March to May), summer (June to August), autumn (September to November), and winter (December to February). Each seasonal dataset is further divided into training, validation, and test sets in a 7:1:2 ratio according to time sequence. The training set is used for solving the opportunity constraints in the first stage, the validation set is used for candidate model selection and parameter optimization in the second stage, and the test set is used for final performance evaluation. The nominal coverage PINC is set to 0.9 in the experiment.

[0262] 2) Hyperparameter selection

[0263] ① Input data dimension: The input lag order for each season was determined through PACF analysis.

[0264] ② Number of hidden layer nodes: The number of hidden layer nodes in each model is determined by grid search.

[0265] ③ Bat Algorithm Hyperparameters: Population size, maximum number of iterations, etc. are determined by grid search.

[0266] 3) Experimental Results

[0267] First, the three candidate interval prediction models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—are compared, and the results are shown in Table 1.

[0268] Table 1 Performance Comparison of RVFL Series Models in Phase 1 (PINC=0.9)

[0269]

[0270] As shown in Table 1, the candidate models with the smallest SCORE are not exactly the same across the four test sets (spring, summer, autumn, and winter), indicating that the suitable RVFL structures differ under different wind power fluctuation scenarios, making automatic screening using multiple candidate structures necessary. After selecting the corresponding first-stage models through SCORE screening, the corresponding PICP and PINAW values ​​were recorded. Furthermore, to verify the effectiveness of the second-stage overall parameter optimization, the optimal basic model obtained from the first-stage screening was optimized using the Bat Algorithm. The results before and after optimization are shown in Table 2.

[0271] Table 2 Performance comparison before and after the second stage optimization (PINC=0.9)

[0272]

[0273] As shown in Table 2, the SCORE further decreased after the second-stage overall parameter optimization on the test sets for all four seasons. This result indicates that after obtaining the basic model that satisfies the coverage constraint in the first stage, further optimization of the random mapping parameters and output weights can reduce the comprehensive evaluation index of the prediction interval and improve the overall performance of the interval prediction.

[0274] Multi-scenario reliability verification: combined with Figures 3-6 Extensive experiments on a seasonal dataset (spring, summer, autumn, and winter) from a European offshore wind farm demonstrate that the proposed first-stage ICCRVFL model, combined with dual reliability constraints, achieves a Predicted Interval Coverage (PICP) close to the nominal coverage (PINC) of 0.90 on all seasonal test sets. This indicates that the proposed method exhibits good interval coverage stability under different seasonal wind power fluctuation scenarios. Figure 7As shown, taking the winter dataset as an example, the second-stage hybrid initialization bat algorithm can continuously reduce the validation set SCORE during the iteration process. The curve decreases rapidly in the early stage of iteration, indicating that the algorithm can quickly search for better parameters based on the elite prior solutions obtained in the first stage; as the number of iterations increases, the rate of decrease in SCORE gradually decreases and tends to stabilize in the later stage, indicating that the optimization process has basically converged. Overall, the second-stage optimization reduces the validation set SCORE from approximately 0.0305 initially to approximately 0.0249, indicating that this stage can further improve the model's comprehensive performance in the prediction interval.

[0275] Two-stage BA global optimization gain analysis: Compared with the single-stage basic ICCRVFL model, after introducing the Bat Algorithm (BA) for second-stage global parameter optimization, the overall evaluation index SCORE on the test set in this wind farm achieved a significant decrease (reduction of 5.1%~15.2%). While maintaining PICP reliability, the prediction interval average width (PINAW) was further effectively compressed. In summary, the BA-ICCRVFL model proposed in this invention achieves good overall performance in balancing prediction interval reliability and sharpness.

[0276] Convergence efficiency and advantages of hybrid initialization: Thanks to the efficient architecture of the RVFL network itself, and the hybrid population initialization strategy of "pre-trained elite solutions + random solutions" adopted in the second stage, the model can quickly locate high-potential feasible regions in the early stage of optimization. Figure 7 This indicates that the proposed method can rapidly reduce the validation set SCORE in the early stages of iteration and gradually converge in the later stages, demonstrating that the hybrid initialization strategy helps improve the stability and effectiveness of the second-stage parameter optimization process and has the potential to meet the application requirements of short-term wind power rolling forecasting.

[0277] In the first stage of this invention, CPLEX is used to solve a chance-constrained mixed-integer programming model to calculate the optimal output weights. Depending on the actual deployment environment, Gurobi, SCIP, GLPK, or other optimization solvers capable of solving mixed-integer linear programming problems can also be used. In the second stage, the Bat Algorithm (BA) is used to globally optimize the overall network parameters. Depending on the actual needs, other swarm intelligence optimization algorithms such as Particle Swarm Optimization (PSO), Differential Evolutionary Algorithm (DEE), Genetic Algorithm (GA), and Whale Algorithm (WAE) can be used instead. Furthermore, this invention employs three candidate structures: basic RVFL, cascaded enhanced RVFL, and direct-connected enhanced RVFL. Depending on the actual prediction target and data complexity, the number of candidate structures can be increased or decreased, or the number of hidden layer nodes, activation function type, and number of hidden layers can be adjusted.

[0278] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A dual-reliability RVFL bat-optimized wind power range prediction method, characterized in that, The steps are as follows: Step 1, Data Acquisition and Sample Construction: Collect historical power data of the target wind farm, and process the historical power data sequentially by handling missing values, correcting outliers, and normalizing to obtain a normalized power sequence; construct input samples and prediction targets based on historical lagged power, and divide them into training set, validation set, and test set according to time order to obtain a dataset used for the first stage model solving, candidate model screening, second stage optimization, and final prediction evaluation; Step 2: Construction of Candidate RVFL Interval Prediction Models: Using the input samples obtained in Step 1 as model input, and the Random Vector Functional Linked Network (RVFL) as the basic predictor, three types of candidate interval prediction models are constructed: basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL. Based on the network structure of each candidate model, corresponding enhancement feature matrices are generated, so that the upper and lower bounds of the prediction interval are represented as linear combinations of the enhancement feature matrices and the output weights, thus obtaining the candidate interval prediction expressions for solving the chance constraints. Step 3, First-stage CPLEX Opportunity Constraint Model Construction: Based on fixing the hidden layer parameters and forming the enhanced feature matrix in Step 2, the upper and lower bounds of the prediction interval for each candidate interval prediction model are represented as a linear combination of the enhanced feature matrix and the output weights. For the three types of candidate models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—opportunity constraint optimization models are established with the goal of reducing the average width of the prediction interval. The opportunity constraint optimization model includes upper and lower bound legality constraints, training set coverage constraints, and validation set coverage constraints, so that the candidate interval prediction models meet the preset reliability requirements on both the training and validation sets. Step 4, First-stage CPLEX solution and basic model selection: The CPLEX solver is used to solve the chance-constrained optimization model corresponding to each candidate model in Step 3. Under the condition of fixed hidden layer parameters, the optimal output weights of each candidate model are obtained, and the candidate models that satisfy the double reliability constraints are obtained. The SCORE index of each candidate model is calculated on the validation set. The SCORE index is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty. The candidate model with the smallest SCORE and that satisfies the reliability constraints is selected as the optimal basic model in the first stage. The hidden layer parameters and optimal output weights of the optimal basic model in the first stage are used as the source of elite prior solutions for the next stage hybrid initialization bat algorithm. Step 5: Second-stage hybrid initialization of the bat algorithm's overall parameters: Using the parameters of the first-stage optimal basic model obtained in Step 4 as the elite prior solution, and combining them with randomly explored individuals to construct a hybrid initialization bat population; the bat algorithm is used to iteratively optimize the overall network parameters of the first-stage optimal basic model, which include random mapping parameters, hidden layer biases, and output weights. After optimization, the final BA-ICCRVFL model is obtained, which provides the final model parameters for interval prediction on the test set. Step 6, Test Set Prediction and Evaluation: The BA-ICCRVFL model optimized in Step 5 is used for test set prediction. The upper and lower bounds of the wind power prediction interval for each test sample are output. The SCORE index, derived from the Winkler score, is used to evaluate the comprehensive performance of the prediction interval, and the wind power interval prediction results and evaluation results are obtained.

2. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Collect historical power data of the target wind farm over a continuous time period. The historical power data includes timestamps and actual active power values. Sort the historical power data according to the timestamp order to form the original power time series. Step 1.2: Preprocess the original power time series: For continuous missing values ​​in the middle of the series, use linear interpolation to fill them in; for missing values ​​at the beginning or end of the series, use forward filling or backward filling; for abnormal power values ​​that are less than zero or exceed the installed capacity range of the wind farm, correct or truncate the abnormal power values ​​to the set power range. Step 1.3: After preprocessing, the power time series is normalized to the [0,1] interval using the Min-Max method, resulting in the normalized power time series. The normalization formula is: in, Let be the original power value at time t. Let be the normalized power value at time t. , These are the minimum and maximum power values ​​in the training data, respectively. Step 1.4: Construct input samples and prediction targets based on the normalized power time series: For prediction time t, the normalized power values ​​of the previous N times form the input feature vector, and the normalized power value at time t is used as the input feature vector. As the prediction target, the expression is: in, Let be the input feature vector of the t-th sample. Let N be the prediction target for the t-th sample; N is the lag order, which is determined by the partial autocorrelation function, validation set search, or fixed historical window length. Step 1.5: Divide the constructed samples into training set, validation set and test set according to time order. The training set is used for solving the opportunity constraint model in the first stage, the validation set is used for candidate model screening and parameter optimization in the second stage, and the test set is used for final interval prediction and performance evaluation.

3. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Set the input sample matrix for: in, Let T be the input feature vector of the t-th sample, and T be the number of samples. Step 2.2: Let the random weight matrix from the input layer to the first hidden layer be... The bias vector of the first hidden layer is The nonlinear activation function is Then the output matrix of the first hidden layer for: in, This only represents the hidden layer bias term. This is a column vector with all elements equal to 1, used for hidden layer feature calculation, and does not represent the output layer bias; Step 2.3: For any candidate model m, let the enhanced feature matrix be denoted as . The output weight matrix is The output weight matrix Including the lower bound of the prediction interval output weight Output weights and the upper bound of the prediction interval The expressions for the lower and upper bounds of the prediction interval are: in, Let be the lower bound vector of the prediction interval for candidate model m. Let be the upper bound vector of the prediction interval for candidate model m. Let m be the enhanced feature matrix of the candidate model. To predict the lower bound of the interval, output weights. Output weights to predict the upper bound of the interval; For the t-th sample, we have: in, and Let be the lower bound and the upper bound of the prediction interval for the t-th sample under the candidate model m, respectively. Let be the enhanced feature vector of the t-th sample under the candidate model m; Step 2.4: To ensure the validity of the output interval, the following constraints are applied to each sample: 。 4. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 3, characterized in that, The specific method for constructing the three types of candidate interval prediction models—basic RVFL, cascaded enhanced RVFL, and direct enhanced RVFL—in step 2 is as follows: (1) Basic RVFL structure Enhanced feature matrix of basic RVFL Defined as the output matrix of the first hidden layer With input sample matrix The concatenation expression is: Lower bound of the prediction interval for the basic RVFL and the upper bound of the prediction interval Generated from output layer weights: In the formula, The lower bound of the prediction interval for the basic RVFL is output as the weight. Output weights as the upper bound of the prediction interval for the basic RVFL; (2) Cascaded Enhanced RVFL Structure Cascaded Enhancement RVFL adds a second hidden layer after the base hidden layer. Let the weight matrix from the first hidden layer to the second hidden layer be... The bias vector of the second hidden layer is Then the output matrix of the second hidden layer for: Enhanced feature matrix of cascaded enhanced RVFL The expression is: Lower bound of the prediction interval for cascaded enhanced RVFL and the upper bound of the prediction interval Generated from the output features of the second hidden layer: In the formula, To enhance the lower bound of the prediction interval of cascaded RVFL, output weights. Output weights for the upper bound of the prediction interval of the cascaded enhanced RVFL; (3) Direct-connected reinforced RVFL structure Direct-connection enhanced RVFL preserves the connections from the input layer, the first hidden layer, and the second hidden layer to the output layer. The enhanced feature matrix of the direct-connection enhanced RVFL... For the input sample matrix First hidden layer output matrix Second hidden layer output matrix The concatenation expression is: Lower bound of prediction interval for direct-connected enhanced RVFL and the upper bound of the prediction interval The expression is: In the formula, To directly enhance the lower bound of the prediction interval of the RVFL, output weights. Output weights to enhance the upper bound of the prediction interval for direct connection to RVFL.

5. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 1, characterized in that, The specific construction method of the first-stage opportunity-constrained optimization model in step 3 is as follows: Step 3.1: Assume the nominal coverage is PINC, and the allowable false negative rate is... satisfy: Step 3.2: Introduce binary overriding variables , is used to indicate whether the t-th sample is covered by the prediction interval, and is expressed as: in, and Let be the lower bound and the upper bound of the prediction interval for the t-th sample under the candidate model m, respectively. This represents the actual power value of the t-th sample. Step 3.3: Use Big-M constraints to characterize the coverage relationship: in, For a constant greater than the set value, since the power value has been normalized to [0,1], we take: Step 3.4, the legality constraints for the prediction interval are: Step 3.5, the training set coverage constraint is: in, The training set is the set of sample indices. The number of samples in the training set; Step 3.6, the validation set coverage constraint is: in, To verify the reliability tolerance coefficient of the set, The set of sample indices for the validation set. The number of samples in the validation set; Step 3.7: For candidate model m, the chance-constrained optimization model solved by CPLEX in the first stage is as follows: in, To predict the lower bound of the interval, output weights. Output weights to predict the upper bound of the interval; Let be the enhanced feature vector of the t-th sample under the candidate model m.

6. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 5, characterized in that, After the CPLEX solution is completed in step 4, the optimal output weights of the candidate model m are obtained. for: The constraints in step 3.7 are satisfied; The corresponding prediction interval is: in, Output weights for the lower bound of the optimal prediction interval of candidate model m. Output weights for the upper bound of the optimal prediction interval of candidate model m. and These are the lower bound and upper bound of the optimal prediction interval for the t-th sample under the candidate model m, respectively.

7. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 6, characterized in that, The specific method for calculating the SCORE index of each candidate model and automatically filtering it in step 4 is as follows: For validation set sample t, the one-sample SCORE of candidate model m is: in, The SCORE value of candidate model m on the validation set sample t; This is an indicator function that takes the value 1 if the condition within the parentheses is true, and 0 otherwise. The average SCORE of candidate model m on the validation set is: Right now: in, The average SCORE value of candidate model m on the validation set; Among the three candidate models, the model with the smallest SCORE is selected as the optimal base model for the first stage: in, Represents the set of candidate models: in, These represent the basic RVFL, cascaded enhancement RVFL, and direct-connect enhancement RVFL, respectively. This is the sequence number of the optimal basic model in the first stage.

8. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 1, characterized in that, The specific method for optimizing the overall parameters of the bat algorithm in the second stage of step 5 is as follows: Step 5.1: Read the parameters of the optimal base model in the first stage and use them as the elite prior vector. The elite prior vector It includes the stochastic hidden layer parameters of the first-stage optimal model and the optimal output weights obtained by CPLEX; Step 5.2, Mixed Initialization of Bat Population: Let the size of the bat population be B, and divide the population into two categories: elite prior individuals and random exploratory individuals; Elite prior individuals are generated by copying the parameter vector of the optimal basic model in the first stage and adding a small Gaussian perturbation, as expressed in the following expression: in, For the first An elite a priori individual, For the disturbance intensity, It is a random vector that follows a standard normal distribution; For the number of elite prior individuals; superscript This indicates that the 0th iteration is the initialization. Randomly explored individuals are generated randomly within the allowed parameter range, and the expression is: in, For the first A random exploration individual, and These are the lower and upper bounds for parameter search, respectively. Let be a random vector whose elements are located in the interval [0,1]. This represents element-wise multiplication; To randomly explore the number of individuals; Let the proportion of elite prior individuals be... The number of elite prior individuals is: The number of individuals to be randomly explored is: Step 5.3: Iteratively optimize the overall network parameters using the bat algorithm; Let the frequency of the i-th bat in the k-th iteration be... ,speed and location Updated to: in, and These are the minimum and maximum frequencies, respectively. A random number in the interval [0,1]. Let be the optimal parameter vector that minimizes the objective function value on the validation set in the population during the (k-1)th iteration. Let be the speed of the i-th bat in the (k-1)th iteration. Let i be the position of the i-th bat in the (k-1)th iteration; During the local search phase, candidate solutions are generated centered on the current optimal solution: in, As a candidate solution, A random number in the interval [0,1]. The average loudness of the current population at the k-th iteration; This is the optimal parameter vector that minimizes the objective function value of the validation set in the population at the k-th iteration. If the objective function value of a candidate solution is better than the current solution, and the random number is less than the current loudness, then the candidate solution is accepted, and the loudness is updated. and pulse emission rate : in, This is the loudness attenuation coefficient. Here, k is the pulse emission rate growth coefficient, and k is the current iteration number. , Let be the loudness of the i-th bat in the k-th and (k+1)-th iterations, respectively. Let be the pulse emission rate of the i-th bat in the (k+1)-th iteration. The initial pulse emission rate; Step 5.4: When the maximum number of iterations is reached or the objective function on the validation set decreases by less than the convergence threshold for several consecutive generations, stop the iteration and output the optimal overall network parameters. .

9. The dual-reliability RVFL bat-optimized wind power range prediction method according to claim 1, characterized in that, The specific methods for test set prediction and evaluation in step 6 are as follows: The optimal network parameters obtained in the second stage optimization For test set Predict and output the prediction range for each test sample: The SCORE metric, derived from the Winkler score, is used as the evaluation metric. For a single sample t in the test set, the single-sample SCORE is: The average SCORE of the test set is : in, The number of samples in the test set. SCORE values ​​for sample t in the test set.

10. A dual-reliability RVFL bat-optimized wind power range prediction system, characterized in that, This system is used to implement the dual-reliability RVFL bat-optimized wind power range prediction method according to any one of claims 1 to 9, the system comprising: The data preprocessing module is used to collect historical power data of the target wind farm, perform missing value processing, outlier correction and normalization processing on the historical power data, and construct input samples and prediction targets based on historical lagging power, and divide them into training set, validation set and test set according to time order. The candidate RVFL model construction module is used to build three types of candidate interval prediction models, namely, basic RVFL, cascaded enhanced RVFL and direct enhanced RVFL, based on the random vector functional linking network RVFL as the predictor, randomly generate and fix the hidden layer parameters, and generate the corresponding enhanced feature matrix. The CPLEX chance constraint output weight solving module is used to establish a chance constraint optimization model for each candidate model with the goal of reducing the average width of the prediction interval, and includes training set coverage constraints and validation set coverage constraints, under the condition that the hidden layer parameters are fixed. The CPLEX solver is used to solve for the optimal output weights of each candidate model. The candidate model automatic selection module is used to calculate the SCORE index of each candidate model on the validation set. The SCORE index is used to comprehensively evaluate the prediction interval width and the out-of-bounds penalty, and select the candidate model with the smallest SCORE and that meets the reliability constraints as the optimal base model in the first stage. The hybrid initialization BA overall parameter optimization module is used to construct a hybrid initialization bat population by using the parameters of the optimal basic model in the first stage as the elite prior solution, combined with random exploration individuals, and iteratively optimizing the overall network parameters using the bat algorithm to obtain the BA-ICCRVFL model. The interval prediction output module is used to use the BA-ICCRVFL model for test set prediction, output the upper and lower bounds of the wind power prediction interval for each test sample, and evaluate the comprehensive performance of the prediction interval using the SCORE index.

Images